How can I create Light Streaks in Cycles?
An alternative method  would be not to use particles, and do the light streaks with curves. It might a bit more tedious to set up, but will not require as much computing power from your machine as particles do.

Give the curve a slight bevel and, by animating the Bevel Factor start and  end  values, you can control how the curve is rendered through the screen . You also have control on the resolution, curvature, start and end points, and you can precisely determine the trajectory. 





EDIT

To change the width at different parts of the curve you can change the radius of the control points:



Add an emissive material to it and some glow on the compositor and you can easily achieve something like this:



If you give the curve some extrusion and bevel and a wild texture



you can have a lot of fun: